RISK MANAGEMENT OF THE INVESTMENT PROJECT AT RANDOM CASH FLOWS

Transcription

1 RISK MAAGEMET OF THE IVESTMET PROJECT AT RADOM CASH FLOWS Tadeusz FRAIK Abstract: In the paper the analytic method of estimation of ris in mining investment projects was introduced. The elementary cash flows were treated as random variables about well-nown schedules of probability. The time of exploitation of project was treated similarly at random. The distribution of net present value of an investment can be described by computing its mean and variance. The expected value and variance yield considerable information about the risiness of the investment. It in method uses the continuous models of cash flows as well as continuous discounting for calculation of net present value. Key words: mining investment projects, ris estimation, random cash flows, random variable probability distribution functions.. Introduction Mining investment operations are accompanied by relatively large riss. Contrary to operations realised in other economic sectors operations concerning mining are characterised by a significant uncertainty both in the nature state, internal conditions and the environment state. The results of a thorough analysis of the project ris constitute a necessary information source for the investor, since the proper identification of the ris and its management allows for successful planning, designing and realisation of the investment. A proper identification and quantification of potential hazard fields is an important element of the project prerealisation study. Examples of hazardous areas charateristic for large mining investments are: - row materials and materials riss, - ris related to the applied technology, - enterprise management ris (process supervision, contractors and performance coordination), - ris related to selecting of subjects present at the investment realisation, - ris related to the realisation (technological breas, variable natural conditions and deposits), - maret ris (changes of the economic situation, cyclical changes of the economic situation), - finance ris (sources of funds, financing structure, paybac system), - credit ris (changes of crediting terms, credit cost, inability to repay a credit), - other misfortunes. M. Wilcze [] considers a project ris management as the art and science of identification, determination and preventing of a ris during the whole project lifetime to be able to effectively realise its aims. The tas of ris management is maximising positive effects and minimising negative consequences of all events. One can spea about a ris when the probability of all events, which can occur, is nown. The ris - in this aspect - can be determined in various ways. This can be a: 845

2 - possibility of sustaining losses, - scatter of expected results, - probability of the result different than the expected, - possibility of occurring of an undesired case, - condition, under which critical states can occur. One of the features of projects realised in mining is the necessity of assuming all riss by an investor and bearing the effects. Other attitudes concerning riss, such as their diversification, compensation, transferring on other subjects or avoiding riss are - in this case - of a limited application [, 3].. Methods taing ris into account applied in the estimation process of investment projects Discount methods are used in estimation processes and analysis of projects. If the net present value (PV) is used for the economic assessment of the project efficiency the two aspects are universally considered to be essential. The first one is the proper estimation of cash flow sizes generated by the project as well as the time in which they occur. The second one is related to the uncertainty of obtaining cash flows on the estimated level in the future. The project analysis with using the PV as the criterion solves, to a significant degree, problems of cash flow sizes and time. The problem related to the project ris estimation is not so straight forward - the PV method does not provide the possibility of direct taing into account the ris related to the project. Several methods of analysis of projects performed under uncertainty conditions can be found in the subject literature. Traditionally these methods are divided into indirect and direct ways of ris taing into account in the project estimation. These methods can be qualified - from the technique point of view - either as deterministic or as probabilistic approaches to ris analysis in the project estimation. The ris, in the probabilistic approach, can be defined as a probability of obtaining unfavourable results. This what is considered unfavourable depends, of course, on what is expected in the given moment. Investments are realised with a hope of obtaining the expected favourable result, often in the indefinite future. This situation causes that all investments are risy, however their essence is never avoiding riss but rather finding the way of their management. The investor inclined to tae a ris prefers the risy investment to caucious one, since the most often it gives a chance for better profits. Simultaneously his inclination to tae a ris, represents a high probability of changing a profit value in relation to the expected value. Therefore, usually, the measure of the possible deviation from the planned profit is applied as the ris measure [4, 5]. For example, in relation to expenditures borne during the investment realisation phase, one can spea about ris when the borne realisation costs of individual objects of the project will be higher than the planned cost estimate.,, lac of ris ris () If the investor has at his disposal the properly large information number it is possible to prepare the statistical description of the borne realisation costs by means of a random variable. 846

3 : ( ) R () On this basis the ris can be defined as the probability of exceeding the assumed price level. R( ) P : ( ) (3) As can be seen, the ris is a function of the assumed cost estimate. If we now the distribution function of the random variable, ( ) P : ( ) f (x) dx (4) The ris can be described as follows: R( ) P : ( ) P : ( ) ( ) (5) Historically speaing, one of the first estimation methods of the project estimation - still readily applied by investors - is the method of expenditures refundation period. The investor bases his decisions on the assumption that the shorter period of the investment expenditures refundation the less risy is the project. When such approach is applied to the investment ris analysis it is assumed that the investment assures positive net cash flows during the paybac period, but cash flows occurring later are still uncertain and in this method practically not existing. Since this method, in its classical form, does not tae into account the time influence on money value changes, does not consider cash flows after the paybac period and does not consider uncertainties of cash flows in the future, it should be considered as not suitable for the ris estimation and not satisfying measure for undertaing investment decisions. Another approach to the ris problem in the project assessment is an application of conventional, deterministic method of the net present value with a discount rate increased by a certain value taing ris into account. The determination of the proper correction for the risfree discount rate as well as the application of point estimations of cash flows in the future (which are then discounted by means of the discount rate taing ris into account) is the main difficulty of this method. However, this method is considered to be better than the paybac period method. A different approach to the ris analysis represents the certainty equivalent method, in which the discount rate free from ris is used for the cash flows actualisation, while the prognosed cash flows are corrected by means of ris coefficients. Since correcting of flows concerns each subperiod taen into account, the determination of certainty equivalent coefficients is one of the basic flaws of this method. Another method, from the deterministic methods group, is the sensitivity analysis, in which an effect of the influence of changes of the ey parameters of the investment project on the level of changes of the measure used for the estimation of the developing venture, is applied. Usually, the maximal and minimal values of the parameter estimation, which can undergo changes during the project lifetime, are taen into account and in such a way, after performing the project estimation, the extreme values of measures used for the estimation 847

4 and variability range of these results, are obtained. The sensitivity analysis is undoubtedly an effective technique supplying a lot of valuable information concerning the project, specially when it is applied together with other methods of ris analysis. The main drawbac of the characterised deterministic methods, is using by them point values of estimations of the future cash flows, which - in addition - are often estimated too optimistically. This concerns very often institutional investors, who want at all costs to substantiate the need (and economic benefit) of the investment realisation. These point values of cash flows estimations do not depict clearly uncertainties, which are - in a natural way - related to the future cash flows. They do not show variability of data characterising the investment project and totally avoid the uncertainty problem. Methods, which in a special way tae into account uncertainties related to the future cash flows, are quite fast developing during the last period. A probability and probability distribution, which using informatics systems provide efficient tools facilitating decision taing due to obtaining much more information, are utilised in these techniques. The main good point of the application of simulation methods for estimations of the efficiency of investment projects is overcoming of losses occurring in deterministic ris analysis methods. The simulation assures more convenient usage of the probability distribution than point estimates of the investigated economic parameter. This technique is elastic in using the selected quality measures and offers a tremendous tool for analysing the project sensitivity. Possibly the most important merit of this technique is the possibility of realisation the project management process by means of the estimated parameters of the probability distribution. In spite of the fact, that the simulation provides special merits in the investment ris estimation and becomes the most lied approach to project managements, it has several shortages. Since it is based on experimental methods it provides only statistical estimations instead of explicit results. Obtaining results by means of these methods is usually a complicated process, since the simulation model has to be developed, computer program written and calculations performed. Another approach, considered in the subject literature [5, 6, 7] as better in the ris estimation, is using the nown probability distribution for the description of cash flows generated by the investment project. This is the analytical way based on properties of statistical distributions, used in order to obtain the probability distribution of the coefficient, which is considered to be the measure of the investment efficiency. The most often such measure constitutes the net present value (PV) or the internal return rate (IRR). It is possible to differentiate, two main cases: net cash flows in successive years of the investment exploitation are independent from each other and these flows are ideally correlated. The second case is much more complex, nevertheless, similarly as in the first one, annual cash flows can be characterised by their expected value and a variance in such a way as to have the probability distribution function of the present value of cash flows at least similar to the normal distribution. In such case it is enough to now only the mean and variance of the present value for the investment project estimation. The ris measure is in this case the variance (in fact: the standard deviation). This way of the ris estimation taes into account uncertainty of information, treating the future cash flows or values from which they depend as random variables. It allows to avoid the computer generation of information in the laborious simulation process, (but does not liberate from the verification concerning the assumed probability distribution function). The most important aspects related to the ris estimation, with taing into consideration the described above approach, are presented in the hereby paper. 848

5 3. Estimation of the investment project when its efficiency measure is a random variable If the PV is used for the economic estimation of the project, its value (assessed deterministically) depends directly only on the net cash flows (CF) and discount rates. The cash flow is then treated as the sequence of discrete cash vectors, concentrated at the end of successive years of the calculation period. If the problem is considered probabilistically, then for the ris estimation of the realised investment project the probability distribution of the net present value should be determined. Such determination should tae into account randomness of cash flows related to the project: investment expenditures flow, net cash flow related to the usage period and residual values flow, corresponding to revenues from sale of redundant capital assets. This cash flow, in large mining investments such as building and mining operations in a new mine, can be related - in practice - to the whole exploitation period and can be considered as the random variable. The period of the investment exploitation, which significantly influences the estimation, can be also treated as the random variable. Randomness of the deposit mining time is related to a certain variability of deposit resources since their size depends on the maret economic situation and on geological deposition of strata. When the continuity of cash flows (which depends from the PV) and the variability of the project service life are taen into account and at the application of continuous discounting, the PV can be the random variable, which expected value can be determined from the following equation [, 8]: E[PV] L L b 0 I I L(n) h(l)dl e I(t) f (I) di e t t f(n)dn dt n K Z Z Z(t)g(Z)dZ e t dt f (n)dn (6) where: I(t) - capital expenditures flow as a time function. The random variable with the probability distribution function f(i), for I I I, Z(t) - refunding of expenditures as a time function. The random variable with the probability distribution function g(z), for Z Z Z, L(n) - residual value of fixed assets in time t = n. The random variable with the probability distribution function L(n), for L L L, n - project duration time treated as the random variable with the probability distribution function f(n), for n, b - investment realisation time, ρ - intensity of continuous interest, ρ= ln( + r), r - discount rate devoid of ris. The above equation can be presented as the sum, which taes into account the expected values of the discussed cash flows: 849

6 E[PV] b 0 E n t t t I(t) e dt EZ(t) e dt f (n) dn EL(n) e f (n) dn (7) b This equation for calculating the net present value consists of three essential parts: investment expenditures flow, net cash flows from the period of the investment usage and capital assets residual value. If distributions of these cash flows are independent the PV variance can be expressed by the following dependence: b n t t n V[PV] V[I(t)]e dt V[Z(t)]e dt V[L(n)]e f (n)dn 0 b (8) where V[I(t)], V[Z(t)] and V[L(n)] denote the variance of investment expenditures flows, net cash flows from the investment exploitation period and capital assets residual value - respectively. The condition for utilising these dependencies for the estimation of riss related to the investment being assessed is the description of cash flows generated by the investments by means of nown distributions (i.e. distributions of nown parameters) or by their combinations. 4. Example of the application of the presented ris estimation procedure for the investment project estimation The example of the application of the presented ris estimation method concerns the management of the part of the deposit in the existing mine. Elementary cash flows, treated as random variables are described by means of the following probability distributions [6,9]: - investment expenditures by the exponential distribution, - flows during the deposit mining period by the monomodal distribution, - residual value by the exponential distribution. The expected PV was determined as the measure of the investment project efficiency and the variance together with the corresponding standard deviation PV - as the ris measure - was calculated for the determined parameters of the given above distributions and for the values on which cash flows depend. As a partial example of the determined analyses parameters influence on the ris level, its dependence on the operation time of the discussed deposit part and on the discount rate level, was presented. It was already mentioned that it was difficult to estimate explicitly the deposit mining time in mining investment projects. The dependence of the ris (standard deviation PV in thousand zl) on the prolongation of the project exploitation time, is shown in Fig.. As can be seen in the diagram the prolongation of this period from to 0 years, (above the initially assumed time), causes the ris increase by more than 73 %. The rate applied for the cash flows actualisation is another value - also characterised by uncertainties - on which the project efficiency significantly depends. At a continuous 850

7 actualisation a discrete discount rate corresponds to the continuous interest intensity, however it is still the constant parameter of the account of the investment efficiency. Both, the efficiency and ris of the investment project are immanently related to the level of this rate. The graphical presentation of the dependence (used as a percentage) of the relative change of the expected PV (efficiency) and standard deviation (ris) on the continuous interest intensity applied for the cash flows actualisation is shown in Fig.. As it is well nown, in the majority of classical investment projects (contrary to the so-called credited projects) the project efficiency decreases when the discount rate increases. This dependence is also seen in the analysed project. However, it occurs that, the increase of the discount rate influences the PV standard deviation much more than the decrease of the expected value Ris Increased exploitation time of the investment project [years] Fig.. Ris dependence on the increased exploitation time of the investment project 85

8 % ,0 0,04 0,06 0,08 0, 0, 0,4 0,6 0,8 0, Continuous interest intensity Expec. value Stand. deviation Fig.. Relative changes of the project efficiency and ris at the increase of the continuous interest intensity This means that projects estimated by means of the relatively high discount rate are characterised by the out-of-proportion lower ris level than it results from the project efficiency decrease. The dependence of the ris measure on the efficiency measure, of the investment project analysed as an example, is presented in Fig. 3 (all values in thousand zl) Ris Efficiency Fig. 3. Relationship between the ris and efficiency of the project at changes of the discount rate 85

9 The relationship presented in the diagram is of the exponential character and can be described by the equation: 0,0009 y 4,748 e x (9) where: y x - standard deviation (ris measure), - expected PV (efficiency measure). This relationship was approximated for variable interest intensity from the range: to 0 %. Its correlation coefficient is very high and equals Conclusions The ris management is one of the fundamental problems related to the investment process. There are various ris sources, however it can be stated that their basic reason is the lac of complete information concerning the future cash flows generated by the project. The problem of the estimation of the ris related to the investment project, when cash flows are treated as random variables is presented in the hereby paper. The base of the estimation of the project efficiency constitutes the expected value of the determined efficiency measure (e.g. the net present value), while the base of the ris estimation is the standard deviation. If the net present value has the distribution similar to the normal distribution then applying the accumulated distribution function maes it possible to determine the probability with which the applied efficiency measure will tae the assumed value. This result will facilitate decision taing by the investor, characterised by the determined approach to riss. The presented method of the calculation of the expected value and the PV variance of the investment project, in contrast to the simulation methods, is based on utilising nown probability distributions and on estimating their parameters for the description of the elementary cash flows generated by the project. The research was supported from MiSW statutory wor: References. Wilcze M. T.: Podstawy zarządzania projetem inwestycyjnym. Wyd. Aademii Eonomicznej w Katowicach. Katowice Brigham E. F., Gapensi L. C.: Zarządzanie finansami, PWE, Warszawa Frani T.: Ryzyo w ocenie efetywności projetów inwestycyjnych w górnictwie, Strategie zarządzania ryzyiem w przedsiębiorstwie wpływ otoczenia na funcjonowanie przedsiębiorstwa, TOiK, Bydgoszcz Ostrowsa E.: Ryzyo projetów inwestycyjnych, PWE, Warszawa Wagle B.: A Statistical Analysis of Ris in Capital Investment Projects, Operational Research Quarterly, Vol. 8, o., Gentry D. W., O eil T. J.: Mine investment analysis, Society of Mining Engineers. ew Yor

10 7. Światowiec-Szczepańsa J.: Ryzyo partnerstwa strategicznego przedsiębiorstwa: ujęcie modelowe. Uniwersytet Eonomiczny w Poznaniu, Poznań Merrett A. J., Syes A. M.: The Finance and Analysis of Capital Projects, Longmans. London Wahl S.: Investment appraisal and economic evaluation of mining enterprise, Trans. Tech. Publications, Houston Hertz D. B.: Ris Analysis in Capital Investment, Harvard Business Review, Vol. 4, McClarnon G. J., Denby B., Schofield D.: The use of virtual reality to aid ris assessment in underground situations, Mining Technology vol. 77, nr 89, Stremole F. J.: Economic evaluation and investment decision methods, Investment Evaluations Corporation, Golden Zinn C. D., Lesso W. G., Motazed B.: A Probabilistic Approach to Ris Analysis in Capital Investment Projects, The Engineering Economist, Vol., o. 4, 977. Dr inż. Tadeusz FRAIK Katedra Eonomii i Zarządzania w Przemyśle AGH Aademia Górniczo-Hutnicza im. St. Staszica Kraów, al. Miciewicza 30 tel.: (0-) frani@agh.edu.pl 854